Texas Go Math Grade 4 Lesson 5.4 Answer Key Use Benchmarks to Determine Reasonableness

Refer to our Texas Go Math Grade 4 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 4 Lesson 5.4 Answer Key Use Benchmarks to Determine Reasonableness.

Texas Go Math Grade 4 Lesson 5.4 Answer Key Use Benchmarks to Determine Reasonableness

Essential Question

How can you find and record sums and differences of fractions?
Answer:

Unlock the Problem

A rover considers many possible paths before choosing the safest path toward its goal. A rover moved yard in a straight line, and then yard around a rock to reach its goal. How far did it travel?
Answer:

Find the sum.

MODEL IT

Use fraction strips.

Think: The rover moved 2 sixth yard and then 5 sixth yard. Shade 2 sixth-size pieces and then 5 sixth-size pieces.

So, the rover traveled _________ yards to reach its goal.
Answer:
So, the rover traveled \(\frac{7}{6}\)  yards to reach its goal.

\(\frac{2}{6}\) + \(\frac{5}{6}\)  = \(\frac{7}{6}\)
So, the rover traveled \(\frac{7}{6}\) yards to reach its goal.

RECORD IT

Write the sum.
_________ + _________ = \(\frac{7}{6}\)
Rename \(\frac{7}{6}\) as a mixed number.
Think: The model shows 1 whole yard and 1 sixth yard.
\(\frac{7}{6}\) = ___________
Answer:
\(\frac{2}{6}\) + \(\frac{5}{6}\)  = \(\frac{7}{6}\)
Rename \(\frac{7}{6}\) as a mixed number.
Think: The model shows 1 whole yard and 1 sixth yard.
\(\frac{7}{6}\) = 1\(\frac{1}{6}\)

Math Talk

Mathematical Processes
Explain how you know \(\frac{5}{6}\) is greater than \(\frac{1}{2}\).
Answer:

Determine whether the sum is reasonable.

Compare the addends to the benchmarks 0, \(\frac{1}{2}\), and 1.

\(\frac{2}{6}\) is greater than \(\frac{1}{2}\). and less than \(\frac{1}{2}\)
The sum is greater than 0 + \(\frac{1}{2}\) = \(\frac{1}{2}\) .
The sum is less than \(\frac{1}{2}\) + 1 = \(\frac{3}{2}\) .
So, 1\(\frac{1}{6}\) is a reasonable sum.
Answer:

\(\frac{5}{6}\) is Greater than \(\frac{1}{2}\) and lesser than 1.

Example

A rover must move \(\frac{5}{8}\) mile to reach its goal. The rover moves \(\frac{1}{8}\) mile toward its goal. How much farther must the rover move to reach its goal?

Answer:
\(\frac{5}{8}\) – \(\frac{1}{8}\) = \(\frac{4}{8}\)

(A) Find the difference.
\(\frac{5}{8}\) – \(\frac{1}{8}\) = \(\frac{4}{8}\)
\(\frac{4}{8}\) farther must the rover move to reach its goal

MODEL IT

Use fraction strips.

So, the rover must ___________ move mile farther.
Answer:

So, the rover must \(\frac{4}{8}\) move mile farther.

RECORD IT

Write the difference.
__________ – ____________ = \(\frac{4}{8}\)
Answer:
\(\frac{5}{8}\) – \(\frac{1}{8}\) = \(\frac{4}{8}\)

(B) Determine whether the difference is reasonable.

Compare the fractions to the benchmarks 0, \(\frac{1}{4}\), \(\frac{3}{4}\), and 1.

\(\frac{1}{8}\) is greater than 0 and less than \(\frac{1}{4}\).
The difference is greater than 0 + \(\frac{1}{4}\) = __________.
The difference is less than \(\frac{1}{4}+\frac{3}{4}\) = ____________.
So, \(\frac{4}{8}\) is a reasonable difference.
Answer:
\(\frac{1}{8}\) is greater than 0 and less than \(\frac{1}{4}\).
The difference is greater than 0 + \(\frac{1}{4}\) = \(\frac{1}{4}\) .
The difference is less than \(\frac{1}{4}+\frac{3}{4}\) = 1.
So, \(\frac{4}{8}\) is a reasonable difference.

\(\frac{5}{8}\) is ____________ than \(\frac{1}{4}\) and __________ than \(\frac{3}{4}\).
Answer:
\(\frac{5}{8}\) is Greater than \(\frac{1}{4}\) and lesser than \(\frac{3}{4}\).

Share and Show

Go Math Lesson 5.4 Answer Key 4th Grade Question 1.
A rover needs to move \(\frac{9}{10}\) mile to a crater. It moves \(\frac{4}{10}\) mile ‘toward the crater. How much farther does it need to move to reach the crater?

• Model the difference.
• Write the difference.

\(\frac{9}{10}-\frac{4}{10}\) = ____________
Answer:

\(\frac{9}{10}-\frac{4}{10}\) = \(\frac{5}{10}\)

Add or subtract. Determine whether your answer is reasonable.

Question 2.
\(\frac{5}{12}+\frac{4}{12}\) = __________
Answer:
\(\frac{5}{12}+\frac{4}{12}\) = \(\frac{9}{12}\)
Explanation:
It is reasonable because \(\frac{9}{12}\) is lesser than 1 and greater than 0

Question 3.
\(\frac{4}{6}-\frac{2}{6}\) = __________
Answer:
\(\frac{4}{6}-\frac{2}{6}\) = \(\frac{2}{6}\)
Explanation:
It is reasonable because \(\frac{2}{6}\) is lesser than 1 and greater than 0

Question 4.
\(\frac{3}{8}+\frac{7}{8}\) = __________
Answer:
\(\frac{3}{8}+\frac{7}{8}\) = \(\frac{9}{8}\)
Explanation:
It is not reasonable because \(\frac{9}{8}\) is Greater than 1 and greater than 0

Unlock the Problem

Go Math Lesson 5.4 Answer Key 4th Grade Question 5.
H.O.T. Apply Multi-Step in our solar system, \(\frac{2}{8}\) of the planets have no moons, \(\frac{1}{8}\) have 1 moon, \(\frac{1}{8}\) have 2 moons, and \(\frac{1}{8}\) have 13 moons. What fraction of the planets have 0, 1, 2, or 13 moons?
(A) \(\frac{5}{8}\)
(B) \(\frac{4}{8}\)
(C) \(\frac{3}{8}\)
(D) \(\frac{2}{8}\)
Answer: A
Explanation:
\(\frac{2}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = \(\frac{5}{8}\)
\(\frac{5}{8}\) fraction of the planets have 0, 1, 2, or 13 moons

a. What do you need to know?
Answer:
fraction of the planets that have 0, 1, 2, or 13 moons.

b. What information are you given?
Answer:
In our solar system, \(\frac{2}{8}\) of the planets have no moons, \(\frac{1}{8}\) have 1 moon, \(\frac{1}{8}\) have 2 moons, and \(\frac{1}{8}\) have 13 moons. Is the information given

c. Write the addition problem you will use to solve this problem.
Answer:
\(\frac{2}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = \(\frac{5}{8}\)

d. Draw a model to help you solve the problem.
Answer:

e. Fill in the bubble for the correct answer choice above.
Answer:
Bubbled the correct the answer

Daily Assessment Task

Fill in the bubble completely to show your answer.

Question 6.
A man times the movement of a banana slug. It moves \(\frac{2}{6}\) foot during the first minute. It then moves \(\frac{3}{6}\) foot during the second minute. How far does the banana slug move in all?
(A) \(\frac{5}{12}\) foot
(B) \(\frac{1}{6}\) foot
(C) \(\frac{1}{12}\) foot
(D) \(\frac{5}{6}\) foot
Answer: D
Explanation:
\(\frac{2}{6}\) + \(\frac{3}{6}\) = \(\frac{5}{6}\) foot
\(\frac{5}{6}\) foot far does the banana slug move in all

Question 7.
One day \(\frac{3}{8}\) of the students in Jack’s class ate toast for breakfast. Another \(\frac{1}{8}\) of the students ate oatmeal. Jack added the fractions and found the sum was \(\frac{7}{8}\). Which statement best describes the sum \(\frac{7}{8}\)?
(A) It is reasonable because \(\frac{1}{2}\) + 0 = \(\frac{1}{2}\).
(B) It is reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1.
(C) It is not reasonable because \(\frac{1}{2}\) + 0 = \(\frac{1}{2}\).
(D) It is not reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1.
Answer: C
Explanation:
\(\frac{3}{8}\) + \(\frac{3}{8}\) = \(\frac{4}{8}\) = \(\frac{1}{2}\).
It is not reasonable because \(\frac{1}{2}\) + 0 = \(\frac{1}{2}\).

Lesson 5.4 Answer Key 4th Grade Go Math Question 8.
Multi-Step Ms. Ryan buys \(\frac{7}{8}\) yard of striped cloth. She uses \(\frac{3}{8}\) yard to make a bag. Then she uses \(\frac{1}{8}\) yard to make a belt. how much cloth does Ms. Ryan have left to make a hat?
(A) \(\frac{2}{8}\) yard
(B) \(\frac{4}{8}\) yard
(C) \(\frac{3}{8}\) yard
(D) \(\frac{6}{8}\) yard
Answer: C
Explanation:
\(\frac{3}{8}\) + \(\frac{1}{8}\)  = \(\frac{4}{8}\)
\(\frac{7}{8}\) – \(\frac{4}{8}\) = \(\frac{3}{8}\) yard
\(\frac{3}{8}\) yard cloth does Ms. Ryan have left to make a hat

TEXAS Test Prep

Question 9.
Suppose a rover on Mars moved \(\frac{2}{6}\) yard in a straight line. Then it moved \(\frac{5}{6}\) yard around a rock, flow many more yards did the rover move around the rock than it moved in a straight line?
(A) \(\frac{3}{12}\) yard
(B) \(\frac{3}{6}\) yard
(C) \(\frac{7}{12}\) yard
(D) 1\(\frac{1}{6}\) yard
Answer: B
Explanation:
\(\frac{5}{6}\) – \(\frac{2}{6}\)  = \(\frac{3}{6}\) yard
\(\frac{3}{6}\)  more yards that the rover move around the rock than it moved in a straight line

Texas Go Math Grade 4 Lesson 5.4 Homework and Practice Answer Key

Question 1.
Melina wants to finish \(\frac{6}{10}\) of her math homework problems before dinner. She finishes \(\frac{4}{10}\) of them. What fraction of her math problems does she still need to complete before dinner?

• Model the difference.
• Write the difference.

\(\frac{6}{10}-\frac{4}{10}\) = ___________
Answer:

\(\frac{6}{10}-\frac{4}{10}\) = \(\frac{2}{10}\)

Add or subtract. Determine whether your answer is reasonable.

Question 2.
\(\frac{1}{6}+\frac{4}{6}\) = ___________
Answer:
\(\frac{1}{6}+\frac{4}{6}\) = \(\frac{5}{6}\)
Explanation:
It is reasonable because \(\frac{5}{6}\) is lesser than 1 and greater than 0

Question 3.
\(\frac{3}{4}-\frac{1}{4}\) = ___________
Answer:
\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{2}{4}\)
Explanation:
It is reasonable because \(\frac{2}{4}\) is lesser than 1 and greater than 0

Go Math Grade 4 Lesson 5.4 Answer Key Question 4.
\(\frac{9}{12}-\frac{3}{12}\) = ___________
Answer:
\(\frac{9}{12}-\frac{3}{12}\) = \(\frac{6}{12}\)
Explanation:
It is reasonable because \(\frac{6}{12}\) is lesser than 1 and greater than 0

Question 5.
\(\frac{3}{6}+\frac{2}{6}\) = ___________
Answer:
\(\frac{3}{6}+\frac{2}{6}\) = \(\frac{5}{6}\)
Explanation:
It is reasonable because \(\frac{5}{6}\) is lesser than 1 and greater than 0

Problem Solving

Question 6.
In Joe’s family, \(\frac{2}{6}\) of the people have blue eves and \(\frac{3}{6}\) of the people have brown eyes. What fraction of people has either blue or brown eyes?
Answer:
\(\frac{2}{6}\) + \(\frac{3}{6}\)  = \(\frac{5}{6}\)
\(\frac{5}{6}\)  fraction of people has either blue or brown eyes

Question 7.
Kim wants to add drawings to \(\frac{5}{8}\) of the stories in her journal. So far she has completed drawings for \(\frac{2}{8}\) of the stories. How many more stories still need drawings?
Answer:
\(\frac{5}{8}\) – \(\frac{2}{8}\) = \(\frac{3}{8}\)
\(\frac{3}{8}\) more stories still need drawings

Lesson Check

Fill in the bubble completely to show your answer.

Question 8.
Add. Determine if the answer is reasonable.
\(\frac{3}{8}+\frac{2}{8}\)
(A) \(\frac{4}{8}\)
(B) \(\frac{3}{8}\)
(C) \(\frac{5}{8}\)
(D) \(\frac{1}{8}\)
Answer: C
Explanation:
\(\frac{3}{8}+\frac{2}{8}\) = \(\frac{5}{8}\)

Go Math Lesson 5.4 4th Grade Answer Key Question 9.
Subtract. Determine if the answer is reasonable.
\(\frac{10}{12}-\frac{1}{12}\)
(A) \(\frac{9}{12}\)
(B) \(\frac{11}{12}\)
(C) \(\frac{8}{12}\)
(D) \(\frac{7}{12}\)
Answer:
\(\frac{10}{12}-\frac{1}{12}\) = \(\frac{9}{12}\)

Question 10.
In Martha’s class, \(\frac{5}{8}\) of the students walk to school and \(\frac{1}{8}\) of the students ride the bus. Martha added the fractions and found the sum was \(\frac{1}{8}\). Which statement best describes the sum \(\frac{1}{8}\)?
(A) It is reasonable because \(v\frac{1}{2}\) + 0 = \(\frac{1}{2}\)
(B) It is reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1
(C) It is not reasonable because \(\frac{1}{2}\) + 0 = \(\frac{1}{2}\)
(D) It is not reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1
Answer: D
Explanation:
It is not reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1

Question 11.
Sabina walks dogs on Saturday. Last Saturday only \(\frac{7}{10}\) of the dogs needed to be walked. She walked \(\frac{5}{10}\) of them in the morning. What fractional part of the dogs does Sabina need to walk in the afternoon?
(A) \(\frac{2}{10}\)
(B) \(\frac{1}{10}\)
(C) \(\frac{3}{10}\)
(D) \(\frac{4}{10}\)
Answer: A
Explanation:
\(\frac{7}{10}\) – \(\frac{5}{10}\) = \(\frac{2}{10}\)
\(\frac{2}{10}\) fractional part of the dogs that Sabina needs to walk in the afternoon

Go Math 4th Grade Practice and Homework Lesson 5.4 Answer Key Question 12.
Multi-Step Luke poured \(\frac{3}{4}\) cup yellow paint into a can and \(\frac{3}{4}\) cup of blue paint in a can. He mixed the colors to make green paint. Then used \(\frac{1}{4}\) cup of the green paint. how much green paint is left?
(A) \(\frac{7}{4}\)cup or 1\(\frac{3}{4}\) cup
(B) \(\frac{1}{4}\)cup
(C) \(\frac{3}{4}\)cup
(D) \(\frac{5}{4}\)cup or 1\(\frac{1}{4}\) cup
Answer: A
Explanation:
\(\frac{7}{4}\)cup or 1\(\frac{3}{4}\) of cup green paint is left

Question 13.
Multi-Step Andrew used \(\frac{2}{12}\) of a carton of eggs for a cake and \(\frac{5}{12}\) of a carton for egg salad, What fraction of the carton is remaining?
(A) \(\frac{4}{12}\)
(B) \(\frac{3}{12}\)
(C) \(\frac{5}{12}\)
(D) \(\frac{7}{12}\)
Answer: D
Explanation:
\(\frac{2}{12}\) + \(\frac{5}{12}\)  = \(\frac{7}{12}\)